Flexural digital material construction and transduction

ABSTRACT

Flexural digital materials are discrete parts that can be assembled into a lattice structure to produce an actuatable structure capable of coordinated reversible spatially-distributed deformation. The structure comprises a set of discrete flexural digital material units assembled according to a lattice geometry, with a majority of the discrete units being connected, or adapted to be connected, to at least two other units according to the geometry. In response to certain types of loading of the structure, a coordinated reversible spatially-distributed deformation of at least part of the structure occurs. The deformation of the structure is due to the shape or material composition of the discrete units, the configuration of connections between the units, and/or the configuration of the lattice geometry. Exemplary types of such actuatable structures include airplane wing sections and robotic leg structures. An automated process may be employed for constructing an actuatable structure from flexural digital materials.

RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.14/201,781, filed Mar. 7, 2014, now U.S. Pat. No. 9,809,001, issued Nov.7, 2017, which claims the benefit of U.S. Provisional Application Ser.No. 61/774,178, filed Mar. 7, 2013, the entire disclosures of which areherein incorporated by reference.

U.S. patent application Ser. No. 14/201,781 is also acontinuation-in-part of U.S. patent application Ser. No. 13/961,880,filed Aug. 7, 2013, now U.S. Pat. No. 9,566,758, issued Feb. 14, 2017,which claims the benefit of U.S. Provisional Application Ser. No.61/680,275, filed Aug. 7, 2012. U.S. patent application Ser. No.13/961,880 is a continuation-in-part of U.S. patent application Ser. No.13/924,530, filed Jun. 21, 2013, now U.S. Pat. No. 9,690,286, issuedJun. 27, 2017, which claims the benefit of U.S. Provisional ApplicationSer. No. 61/662,358, filed Jun. 21, 2012, and is also acontinuation-in-part of U.S. patent application Ser. No. 13/277,103,filed Oct. 19, 2011, now U.S. Pat. No. 8,986,809, issued Mar. 24, 2015,which claims the benefit of U.S. Provisional Application Ser. No.61/394,713, filed Oct. 19, 2010, the entire disclosures of which are allherein incorporated by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with U.S. government support under Contract No.W911NF-11-1-0096, awarded by the Army Research Office, and underContract No. HR0011-12-1-0003, awarded by the Defense Advanced ResearchProjects Agency. The Government has certain rights in this invention.

FIELD OF THE TECHNOLOGY

The present invention relates to digital materials and, in particular,to construction using flexural digital materials.

BACKGROUND

Continuously shape-morphing structures have previously mostly focused ontraditional kinematics with flexural components that match or exceed thedeformation length scales, and/or rely on high density and high costmaterials such as piezoelectric ceramics, shape memory alloys, andelectro-active polymers. This has limited the size, degrees of freedom,and manufacturability of shape-morphing structures to date.

Conventionally designed and engineered fabrication methods employdigital computation and communication algorithms to control analogmechanical equipment that additively or subtractively forms shapes frommasses of bulk material. Digital material systems instead propose amethod for fabrication from discrete parts with discrete relative localpositioning, instead of continuous variation of composition and locationof material, as in an analog fabrication system. This may be thought ofas printing, noting that an important distinction between digitalmaterial printing and conventional commercially available threedimensional printing processes is that digital material printing isreversible, and the information regarding the shape, assembly, andfunction of a finished product is intrinsic to the material that it iscomposed of.

Structure design and construction requires consideration of multiplefactors. The design and fabrication process will generally includeconsiderations of: 1) design requirements, 2) likely failure modes, 3)stress analysis for failure modes identified, 4) material selection andbehavior, 5) fabrication, and 6) testing, all within the context of theoverall design goals. For example, in order to achieve reduction inweight, increase in strength, and reduction in cost, the engineeringdesign, materials of construction, and methods of fabrication must allbe considered. In general, modern fabrication techniques include variousadditive and subtractive processes, employing a range of materials,including, but not limited to, composite materials, cellular materials,and digital materials.

“Composite materials” describes any two or more materials that arecombined together in a single bulk material to obtain the bestproperties from both materials. Many industries are shifting towards theuse of more composite materials because they display the single mostsignificant consideration for any application: low weight compared tostrength. The material properties of composites are unlike any materialthus far, because they combine the properties of a high modulus and hightensile strength fiber for flexibility and strength, with a low modulusstiff matrix which transfers forces from one fiber to the next, creatingessentially a continuous analog bulk material. Fiber-reinforcedcomposite materials have thus enabled construction of structures havinglarge reductions in weight for given strength and stiffness targets, butthis reduction comes at the cost of very high design and processingcosts and many challenges in producing mechanical interfaces (joints).

Composites are still problematic as the material of choice hinderingwidespread use for many reasons. First, composites vary in fibers,resins, and weaves from one manufacturer to the next, with strength andweight dependent on layup and direction of weave. Second, compositesrequire an energy intensive process. Highly skilled technicians arenever really able to have complete control over the application ofpressure and heat to allow for proper curing and even distribution ofheat over the entire surface [Dorworth, C. Louis, Gardiner L. Ginger,Mellema M. Greg, “Essentials of Advanced Composite Fabrication andRepair”, 2010]. Third, any flaw detected in a composite skin renders theentire material a complete waste, or makes repair difficult sincecreating the exact conditions to maintain bond strength is close toimpossible to achieve. Fourth, not only is the composite surfacedesigned, but the tooling and moulding for the composite is just asintensive as the final part. In the process of mitigating stressconcentration, composite skins are ultimately labor intensive, timeintensive, and expensive.

“Cellular materials” or “cellular solids” refers to the materialstructure of any living or nonliving matter, typically described asanisotropic and unidirectional or isotropic and having the sameproperties in all directions. Cellular materials can fill space intwo-dimensions as extruded honeycomb or prismatic cells orthree-dimensions as space filling polyhedra in various latticeformations. Cellular materials have been mimicked in engineered foamcore structures used in construction, aerospace, and medical industries.These man made materials can be designed as highly porous scaffolds orfully dense structures which can be mechanically tuneable for a specificperformance. While the science of cellular solids has enabled widespreaduse of lightweight materials to meet many important engineering needs,such as passive energy absorption, cellular solids are not presently inwidespread use for structural applications, perhaps due to a large gapbetween the strength and stiffness to weight ratios of popular classicalsolids and the performance of known lightweight cellular materialsproduced from the same constituent material.

The science of cellular solids has enabled the widespread use oflightweight materials to meet important engineering needs, such aspassive energy absorption, but they are not in widespread use forstructural applications, perhaps due to a large gap between the strengthand stiffness to weight ratios of popular classical solids, and theperformance of known lightweight cellular materials that are producedfrom the same constituent material. The engineering of fiber reinforcedcomposite materials has enabled structures with large reductions inweight for given strength and stiffness targets, but at very high designand processing costs, and many challenges in producing mechanicalinterfaces (joints).

The advances of material science in engineering of cellular solids, suchas honeycomb core materials and foams, have resulted in the ability todesign with lighter, more elastic, more insulating, and more energyabsorptive materials. The practice of treating cellular solids asconventional continuous solids allows for simple application withconventional engineering and design methods. In the context of cellularmaterials, it has been noted that “constructed” periodic metal latticesallow for much larger cell size, and therefore lower relative density,compared to other methods of producing cellular metals [Wadley, H.,“Cellular Metals Manufacturing”, Advanced Engineering Materials, vol. 4,no. 10, pp. 726-733, 2002].

Digital materials are comprised of a small number of types of discretephysical building blocks, which assemble to form constructions that meetthe versatility and scalability of digital computation and communicationsystems. Digital materials have specifically been defined in prior workby Popescu as having three main properties at the highest level ofdescription: a finite set of components or discrete parts, a finite setof discretized joints of all components in a digital material, andcomplete control of assembly and placement of discrete interlockingcomponents [Popescu, G., Gershenfeld, N. and Marhale, T., “DigitalMaterials For Digital Printing”, International Conference on DigitalFabrication Technologies, Denver, Colo., September 2006]. Digitalmaterials promise scalable methods of producing functional things withreconfigurable sets of discrete and compatible parts.

Digital Cellular Solids are cellular solids that exhibit improvements inrelative stiffness and strength compared to relative density, overcurrent practices for producing lightweight materials. This isaccomplished by assembling lattice geometries that perform better thanany currently made with traditional methods. When implemented with fibercomposites, the result is not only stiffer and stronger than anypreviously known ultra-light material, but it presents a new scalableand flexible workflow for applying fiber composites to engineeringproblems.

Digital composites allow for rapid prototyping of fiber composite partswith high throughput robotic digital assemblers. The individualcomponents may be produced through conventional means, as suited formass production of identical parts. With digital assembly of sparsevolumes composed of many smaller components, all of the tooling requiredmay be significantly smaller than the finished assemblies. The possibleproperties of digital materials are myriad, and they can be designed outof any material using existing fabrication technologies and tools inorder to build cellular structures for any application. Digitalmaterials, as compared to analog materials, are completely reversible,eliminating waste by allowing individual parts to be reused and recycledat any point in the product lifecycle, no matter how large the assembly.

Architecture and civil engineering have employed space frame trussstructures for many years. These have not previously been scaledvolumetrically, as a perfect lattice, to the orders of units that makeit practical to consider the bulk assemblies as a continuum, as would bebeneficial for engineering and design purposes. Further, it is wellknown that space frames with many elements sharing structural dutypossess highly desirable characteristics in terms of failure modes anddamage tolerance [Lakes, R., “Materials with structural hierarchy”,Nature, vol. 361, pp. 511-515, 1993; Huybrechts, S., & Tsai, S. W.,“Analysis and Behavior of Grid Structures”, Composites Science andTechnology, vol. 56, pp. 1001-1015, 1996]. This is evident in “geodetic”airframe designs [Paul, D., Kelly, L., Venkaya, V., & Hess, T.,“Evolution of U.S. Military Aircraft Structures Technology”, Journal ofAircraft, vol. 39, no. 1, pp. 18-29, 2002]. The current state of roboticmanufacturing technology makes it easy to see how massively parallelassembly of digital materials can be implemented, including the assemblyof structures that are larger than the assembly machinery.

The commercial aerospace industry has been moving towards aircraftdesigns that have fewer but larger monolithic fiber composite parts, inorder to produce highly tuned and lightweight structural systems thatmeet extreme service, monitoring, and general environmentalrequirements. Conventional wisdom is that larger monolithic parts arebetter than an assembly of smaller parts because producing effectivejoints between parts is highly problematic in practice. Conventionalmanufacturing processes have scaled up, accordingly, which requirestools (e.g., molds for defining the shape of the part), and ovens (e.g.,autoclaves for polymer matrix curing) that are large enough to influencethe size of the buildings that must contain them. Some may consider thatthe expense involved with these manufacturing methods limits theindustry altogether; there is no question that it limits prototypingcapabilities. Further, the per-part investment is high enough to warrantcomplex repair processes as defects of small relative size arise, to saynothing of their contribution to resource intensive qualificationprocedures [U.S. Department of Defense, Composite Materials Handbook,“Polymer Matrix Composites Guidelines for Characterization of StructuralMaterials”, MIL-HDBK-17-1F 1, 2002].

Leung [Leung, A. C. H., “Actuation of kagome lattice structures”,American Institute of Aeronautics and Astronautics, April 2004] showedthat the Kagome lattice structure is a desirable starting point forlattice based active structures in two dimensions. Unfortunately, therewas little time given to manufacturing considerations or materialproperties. Hutchinson [Hutchinson, R. G., N. Wicks, A. G. Evans, N. A.Fleck, J. W. Hutchinson, “Kagome plate structures for actuation”,International Journal of Solids and Structures, 2003, vol. 40, pp.6969-6980] continues this line of inquiry, using double-layer Kagomelattices. Theoretical bounds on performance are derived, but similarlylittle consideration is given to fabrication, save one mention of atransient liquid phase bonding process. Both of these approaches arebound to plate-like structures, as opposed to the space-filling latticesof this approach.

Donev [Donev, Aleksandar, Salvatore Torquato, “Energy-efficientactuation in infinite lattice structures”, Journal of Mechanics andPhysics of Solids, 2003, vol. 51, pp. 1459-1475] takes a more generalstance, showing that it is possible to design lattice structures thatreach any uniform stress state in two or three dimensions by actuating aset of bars in coordination while doing zero work. This bar actuationparadigm is characteristic of all known lattice actuation literature(including those of the previous paragraph), which differs from theglobal actuation framework presented here. Despite this difference, theresults are very exciting. If the actuated bars are replaced withflexural degrees of freedom, any uniform strain can be achieved at onlythe small energy cost of deforming the flexural elements.

SUMMARY

Bulk digital composites lie in a regime of density and stiffness faroutside the parameter space of conventional materials. Such digitalcomposites are used in deformable, actuatable structures that combinethese desirable material properties with a specified deformation. Theseactuators exhibit spatially distributed deformation, with drive massseparated from moving regions, and are capable of exotic, programmablemovements. These digital material actuators are controlled globally,usually with an internally routed tendon. Like an animal muscle,opposing pairs of these tendons give stiffness to the structure whenstressed equally. When differentially stressed, they produce theprescribed deformation. Spatially distributed actuation withoutdiscontinuities holds particular promise for the design of efficientaerodynamic control surfaces. For high-speed applications, this class ofactuators has drastically lower moving mass than conventional approachesin robotics, enabling much higher slew rates. Finally, while the rangeof programmable deformations scales exponentially with lattice size, themanufacturing complexity scales only linearly or sublinearly through theautomation made possible by the small part set.

In one aspect, the invention is an actuatable structure comprising a setof discrete units, the set of discrete units being assembled into thestructure according to a lattice geometry, wherein a majority of thediscrete units are each connected, or adapted to be connected, to atleast two other units in the set according to the lattice geometry, andwherein, in response to at least one type of loading of the structure, acoordinated reversible spatially-distributed deformation of at leastpart of the structure occurs. The coordinated reversiblespatially-distributed deformation of at least part of the structure isdue at least in part to the shape of the units in the set, the materialcomposition of the units in the set, the configuration of connectionsbetween the units of the set, and/or the configuration of the latticegeometry. The connections may be elastic. The units in the set ofdiscrete units may be identical or of more than one type, and some ofthe types may be connector units. When there is more than one type ofunit, different types of units may differ in material composition orproperty from other types of units. Some of the discrete units may beconnected to others of the discrete units by connections that areadapted to transfer force between connected units. The structure mayhave step-function flexures configured to protect the integrity of thelattice.

In one aspect of the invention, the actuatable structure may be adigital material wing and the structure has sufficient flexural degreesof freedom to vary camber and produce a continuous spanwise twist. Inanother aspect of the invention, the actuatable structure may be arobotic leg having at least one tendon configured for actuating the legand the leg may have sufficient flexural degrees of freedom to producecoordinated buckling modes and corresponding elastic energy storage.

In yet another aspect of the invention, an automated process forconstructing an actuatable structure includes the steps of assembling aset of discrete units into the structure by connecting a majority of theset of discrete units to each other, each of the discrete units beingconnected, or adapted to be connected, to at least two other units inthe set according to a lattice geometry, and assembling the connecteddiscrete units into the structure according to the lattice geometry,wherein the assembled connected set of discrete units forms thestructure and wherein the structure has the property that, in responseto at least one type of loading of the structure, a coordinatedreversible spatially-distributed deformation of at least part of thestructure occurs. The process may be controlled by a specially adaptedprocessor implementing a computer algorithm. The mechanical propertiesof the structure produced by the process may be tuned by changing theratio of different types of the discrete units used to assemble thestructure, the shape of the different types of the discrete units usedto assemble the structure, the mechanical properties of the differenttypes of the discrete units used to assemble the structure, and/or thelattice geometry of the structure.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, advantages and novel features of the invention willbecome more apparent from the following detailed description of theinvention when considered in conjunction with the accompanying drawingswherein:

FIGS. 1A-D depict the construction of an exemplary digital materialairplane wing section prototype having variable aerodynamic modes,according to one aspect of the present invention;

FIG. 2 is a graph of lift to drag ratio (L/D) vs. velocity for theprototype of FIG. 1D;

FIG. 3 depicts differential deformation of the prototype of FIG. 1Dunder experimental conditions;

FIGS. 4A-D depict an example of filling an arbitrary wing sectionprofile with unique digital material piece types;

FIG. 5 depicts stacks of exemplary different piece types suitable foruse in constructing an item having a cylindrical geometry;

FIG. 6 depicts an exemplary airplane filled with identical digitalmaterial pieces;

FIG. 7 is a close up view of one segment of the lattice construct of theairplane of FIG. 6;

FIGS. 8A-C depict an exemplary flexural digital material leg thatexhibits large strain in one direction while maintaining lengthwise andoff-axis stiffness;

FIG. 9 illustrates the stride sequence of a pair of exemplary roboticdigital material legs constructed according to one aspect of theinvention;

FIGS. 10, 11A-B, 12A-B, and 13 are design drawings for a digitalmaterial leg, such as the leg of FIG. 9; wherein:

FIG. 10 depicts the exemplary part set for the digital material leg;

FIGS. 11A-B depict exemplary design drawings for constructions for thedigital material leg using the parts of FIG. 11A-B;

FIGS. 12A-B are 3D design renderings of parts of the lattice structureof the digital material leg; and

FIG. 13 is a 3D design drawing of a complete set of the legs;

FIG. 14 depicts an exemplary prototype step-function shearing flexurewith dovetail keys;

FIGS. 15A-B depict the flexure of FIG. 14 at zero (FIG. 15A) andprescribed (FIG. 15B) strain;

FIGS. 16, 17A-F, and 18A-B depict various experiments and simulationsperformed to measure and model flexural digital material part behavior,in order to build a hierarchical finite element model; and

FIGS. 19 and 20 depict hierarchical simulations of exemplaryconstructions using flexural digital materials.

DETAILED DESCRIPTION

In one aspect of the invention, digital composites are used to implementactuators exhibiting spatially distributed deformation, with actuatormass separated from moving regions, and capable of exotic, programmablemovements. Bulk digital composites have been fully described andimplemented in U.S. patent application Ser. No. 13/961,880, filed Aug.7, 2013, of which this application is a continuation-in-part and whichis herein incorporated by reference in its entirety, and in Cheung, K.C., “Digital Cellular Solids: Reconfigurable Composite Materials”, Ph.D.Thesis, Massachusetts Institute of Technology, 2012, and Cheung, K. C.,Gershenfeld, N., “Reversibly Assembled Cellular Composite Materials”,Science vol. 22, May 2013, which are also herein incorporated byreference in their entirety.

U.S. patent application Ser. No. 13/961,880 and Cheung and Gershenfeld(2013) show that bulk digital composites lie in a regime of density andstiffness far outside the parameter space of conventional materials.Further, materials assembled this way are useful as deformable,actuatable structures. Flexural degrees of freedom can be placed intothe discrete lattice to induce a desired global behavior in response tospecific loads and driving forces. The same part set can be assembled inmultiple ways to produce different bulk responses to the same externalload. While these lattices can exhibit the high stiffness of atension-dominated structure under some assembly conditions, flexuraldegrees of freedom can be placed to encourage desired coordinatedbuckling modes and the corresponding elastic energy storage.

The present invention demonstrates the applicability of a digitalmaterial approach in designing new methods for assembly of structureswith static reconfigurability. As a digital material system, digitalflexural materials are kits-of-parts with few primitive part types thatcan produce functionally useful assemblies, which have life cycleefficiencies exceeding that of conventional engineered fabricationmethods. Digital materials allow for the design of materials with manysmall and inexpensive flexures that combine to deliver largedisplacements with large forces, and/or tunable elastic phases in alattice geometry that allows for deformation with simple large scaleactuation without compromising the strength of the assembly.

In many applications, this type of actuation holds advantages overconventional actuation. First, the deformation is spatially distributed,resulting in actuation without discontinuities. This holds particularpromise for the design of aerodynamic control surfaces. Second, forhigh-speed applications, this class of actuators has low moving mass.One application is fast-moving robotic legs where all motor mass isconfined to a stationary hip and motion is transmitted along two digitalmaterial actuators in series using tendons and cable housing.

An exemplary application of the invention is aerodynamic devices, suchas aircraft wings. Variable geometry mechanisms have been employed inmany fields including structural and vehicle (sea, air, or land) design.The purpose is often to adapt to varying environmental physicalconditions, and the devices themselves are typically active and havebeen implemented with extrinsic control and actuation. Digital materialsallow for structures with similar changes in geometry by design, butwhich occur as continuous deformations and, possibly, as passiveresponses to changes in environmental condition. Current control andactuation systems are extrinsic to the primary aircraft structure. Awing having a digital flexural material structure can be tuned topassively elastically deform to desired shapes as a response to changesin load, load distribution, or pressure that results from changes inairspeed, while maintaining structural integrity.

FIGS. 1A-D depict the construction of an exemplary digital materialairplane wing section prototype having variable aerodynamic modes. Thisprototype digital material wing has the flexural degrees of freedom tovary camber and produce a continuous spanwise twist. These modes arefundamental to aerodynamic control and avoid efficiency losses fromdiscontinuous control surfaces. Shown in FIG. 1A are exemplary parts 105and basic unit shape 110 constructed from parts 105. FIGS. 1B and 1C aretwo views of a portion of the airplane wing internal latticeconstruction from parts 105 and basic unit shapes 110. FIG. 1D depictsthe completed airplane wing section prototype 140. FIG. 2 is a graph oflift to drag ratio (L/D) 210 vs velocity 220 for the prototype of FIG.1D under high camber 230 and low camber 240 conditions. FIG. 3 depictsdifferential deformation of the prototype of FIG. 1D under experimentalconditions. Depicted in FIG. 3 are high camber 310, low camber 320, roll(−) 330, and roll (+) 340.

These lattice materials can be made to follow a precisely describedsurface (such as those used in aeronautics) by specifically designingindividual parts to follow a specified path. FIGS. 4A-D depict anexample of filling an arbitrary NACA (National Advisory Committee forAeronautics) wing section profile with unique piece types.

Using this system, even items with highly complex geometries, such ascylindrical, can be constructed. FIG. 5 depicts stacks of five differentexemplary piece types 510, 520, 530, 540, 550 suitable for use inconstructing an item having a cylindrical geometry.

Complex geometries with less precisely specified contours can be filledwith uniform pieces, lowering the complexity of robotic assembly. FIG. 6depicts an exemplary airplane filled with identical digital materialpieces, while FIG. 7 is a close up view of one segment of the airplaneconstruction.

Structures according to the invention are also applicable to robotics.FIGS. 8A-C depict an exemplary flexural digital material leg thatexhibits large strain in one direction while maintaining remarkablelengthwise and off-axis stiffness. In FIG. 8A, digital material leg 810is unloaded. In FIG. 8B, leg 810 shows minimal compression under a 25lb. weight 820, yet in FIG. 8C it can be seen that leg 810 is capable offlexions in excess of 60 degrees.

FIG. 9 illustrates the stride sequence of a pair of exemplary roboticdigital material legs 910, 920 constructed according to one aspect ofthe invention. Legs 910, 920 are actuated using the exemplary basicactuator 810 of FIGS. 8A-C. Each leg 910, 920 uses two such segments tomake a double pendulum, capable of making efficient strides. The legsare driven with tendons running through the structure. Such roboticlimbs exhibit precisely constrained, complex motion with extremely lowmoving mass. Due to this, the potential stride rates could be very high.In the embodiment of FIG. 9, each leg has four degrees of freedom, eachactuated with a tendon. The first two tendons actuate the hip in theupper leg, while remaining two are communicated through cable housing tothe knee in the lower leg.

FIGS. 10, 11A-B, 12A-B, and 13 are design drawings for a digitalmaterial leg such as the exemplary leg of FIG. 9. FIG. 10 depicts theexemplary part set, having parts 1010, 1020, 1030, 1040. The horizontaldistance 1110 between flexures is preserved when the leg is stretchedvertically 1120. The central spine 1130 is comprised of parts 1030 andresists compression, while flexures 1040 allow bending 1140. FIGS. 11A-Bdepict design drawings for constructions using parts 1010, 1020 (FIG.11A) and parts 1030, 1040 (FIG. 11B). FIGS. 12A-B are 3D designrenderings of parts of the lattice structure, and FIG. 13 is a 3D designrendering of the complete set of legs. As FIG. 13 shows, motors 1310 arecontained at hips 1320, 1330 (actuation ˜sin(t)). With knees 1340, 1350having actuation ˜sin²(t), and tendon actuation 1360 as shown, the legshave a double pendulum gait 1370.

These digital material actuators, such as for the leg of the previousexamples, are controlled globally, usually with an internally routedtendon. Like an animal muscle, opposing pairs of these tendons givestiffness to the structure when stressed equally. When differentiallystressed, they produce the prescribed deformation. Far from theequilibrium position of the lattice, the integrity of the lattice can beguaranteed by using flexures that lock out at a prescribed strain. FIG.14 depicts an exemplary prototype step-function shearing flexure withdovetail keys. As shown in FIG. 15A, around zero strain, the wholeflexure exhibits behavior characteristic of the five thin strips. At aprescribed strain (FIG. 15B), however, the keys engage and provide thestiffness of nearly the entire plywood member.

Assembling complex shapes through deformation. This technique may alsobe used to produce complex geometry from the flexed state of a simplerlattice. If done correctly, this can also desirably pre-stress membersin the lattice. One interesting use case for this is the construction ofvacuum balloons, lightweight, skinned structures from which air can beevacuated without collapse. First order physical analysis suggests asuccessful vacuum balloon could employ a cylindrical lattice structure,several unit cells thick, with radius on the order of 1-10 meters. Thisdesign could be assembled in a flat state with simplified constructiontechniques and then deformed into the cylindrical configuration.

Predicting performance. When digital material structures are designedwith many parts from a small number of piece types, a built-inopportunity to model at the part level occurs. The finite elementsbecome the pieces themselves, allowing verification of the analysis bytesting the physical finite elements. The result of modeling and testingparts, is a trusted element stiffness matrix for the digital materialpiece. For any assembly of these parts, a global stiffness matrix can beaggregated and the resulting system solved. This technique permitsproduction of accurate predictions without meshing entire assemblies onthe scale of airplanes. This is a drastic reduction in computationalburden and eliminates opportunities for model failures.

FIGS. 16, 17A-F, and 18A-B depict various experiments and simulationsperformed to measure and model flexural digital material part behavior,in order to build a hierarchical finite element model. FIGS. 19 and 20depict hierarchical simulations of exemplary constructions usingflexural digital materials.

Back-action sensing of flexural digital materials. Discrete assembly ofdigital material permits programming of a complex deformation mode andactuation of it with a simple global boundary condition, but this alsopermits sensing of complex deformation modes by including force andtorque measurements on the boundary conditions. For instance, thedeformable wing shown above could sense lift conditions by including astrain gauge in series with the camber actuator. In this way, deformabledigital materials enable a large class of devices to sense interactionswith the external environment by monitoring the prescribed deformationmodes.

While preferred embodiments of the invention are disclosed herein, manyother implementations will occur to one of ordinary skill in the art andare all within the scope of the invention. Each of the variousembodiments described above may be combined with other describedembodiments in order to provide multiple features. Furthermore, whilethe foregoing describes a number of separate embodiments of theapparatus and method of the present invention, what has been describedherein is merely illustrative of the application of the principles ofthe present invention. Other arrangements, methods, modifications, andsubstitutions by one of ordinary skill in the art are therefore alsoconsidered to be within the scope of the present invention, which is notto be limited except by the claims.

What is claimed is:
 1. An automated process for constructing anactuatable structure, comprising: assembling a set of discrete unitsinto the structure by: connecting a majority of the set of discreteunits to each other, wherein a majority of the discrete units areconnected, or are connectable, to at least two other of the discreteunits of the set of discrete units; and assembling the connecteddiscrete units into the structure according to a lattice geometry,wherein the structure has a property of strength of the structure andthe lattice geometry allows for reversible deformation of at least partof the structure without compromise of the strength of the structure,wherein the assembled connected set of discrete units forms thestructure and wherein the structure has a property that a coordinatedreversible spatially-distributed deformation of at least part of thestructure occurs in response to changes in load or actuation.
 2. Theautomated process of claim 1, wherein the mechanical properties of thestructure produced by the process may be tuned by changing one or moreof: at least one ratio of different types of the discrete units used toassemble the structure, at least one shape of the different types of thediscrete units used to assemble the structure, at least one mechanicalproperty of the different types of the discrete units used to assemblethe structure, and the lattice geometry of the structure.
 3. Theautomated process of claim 1, wherein the automated process iscontrolled by a specially-adapted processor implementing a computeralgorithm.
 4. The automated process of claim 3, wherein the mechanicalproperties of the structure produced by the process may be tuned bychanging one or more of: at least one ratio of different types of thediscrete units used to assemble the structure, at least one shape of thedifferent types of the discrete units used to assemble the structure, atleast one mechanical property of the different types of the discreteunits used to assemble the structure, and the lattice geometry of thestructure.
 5. The automated process of claim 1, wherein at least some ofthe discrete units are connected to others of the discrete units byconnections that are adapted to transfer force between the connecteddiscrete units.
 6. The automated process of claim 5, wherein at leastsome of the connections are elastic connections.
 7. The automatedprocess of claim 1, wherein the units in the set of discrete units areidentical.
 8. The automated process of claim 1, wherein the units in theset of discrete units are of at least two types.
 9. The automatedprocess of claim 8, wherein at least one of the at least two types ofunits is a connector unit.
 10. The automated process of claim 8, whereinat least one of the at least two types of units differs in materialcomposition or property from at least another of the at least two typesof units.
 11. The automated process of claim 1, wherein the actuatablestructure constructed is a digital material wing and the structure hassufficient flexural degrees of freedom to vary camber and produce acontinuous spanwise twist.
 12. The automated process of claim 1, whereinthe actuatable structure constructed is a robotic leg, the robotic legfurther comprising at least one tendon configured for actuating the legand wherein the leg has sufficient flexural degrees of freedom toproduce coordinated buckling modes and corresponding elastic energystorage.
 13. The automated process of claim 1, wherein the latticegeometry of the structure has an integrity and the actuatable structureconstructed further comprises step-function flexures configured toprotect the integrity of the lattice geometry of the structure.
 14. Theautomated process of claim 1, wherein the coordinated reversiblespatially-distributed reversible deformation of at least part of theactuatable structure is due to at least in part to at least one of: atleast one shape of the units in the set, at least one materialcomposition of the units in the set, at least one configuration ofconnections between the units of the set, and at least one configurationof the lattice geometry.
 15. The automated process of claim 14, whereinat least some of the discrete units are connected to others of thediscrete units by connections that are adapted to transfer force betweenthe connected discrete units.